Articles publicats en revistes (Matemàtiques i Informàtica)

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Instanton bundles vs Ulrich bundles on projective spaces
(Springer, 2021-06-01) Costa Farràs, Laura; Miró-Roig, Rosa M. (Rosa Maria)
We relate the existence of rank $r$ Ulrich bundles on a Veronese 3-fold $\left(\mathbb{P}^3, \mathcal{O}_{\mathbb{P}^3}(d)\right)$ with the existence of rank $r$ instanton bundles on $\mathbb{P}^3$. This relation will allow us to prove the existence of rank $r$ Ulrich bundles on $\left(\mathbb{P}^3, \mathcal{O}_{\mathbb{P}^3}(d)\right)$ for certain values of $(d, r)$. For instance, we explicitly determine the integers $r$ such that rank $r$ Ulrich bundles on $\mathbb{P}^3$ for the Veronese embedding $\mathcal{O}_{\mathbb{P}^3}(3)$ exist and, in particular, we solve the first open case of Conjecture 4.1.
Clifford's theorem for coherent systems on surfaces with Kodaira dimension $\kappa \leq 0$
(Springer Nature, 2025-08-21) Costa Farràs, Laura; Macías Tarrío, Irene; Roa-Leguizamón, Leonardo
Let $X$ be a smooth irreducible projective surface with Kodaira dimension $\kappa \leq 0$. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on $X$.
‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
(Elsevier Masson, 2025-10-01) Antonelli, Vincenzo; Malaspina, Francesco; Marchesi, Simone; Pons Llopis, Joan
In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable 't Hooft bundles for each admissible charge $k$. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge $k$. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in $F$ as well as the family of del Pezzo surfaces realized as hyperplane sections of $F$. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.
Brill-Noether theory of stable vector bundles on ruled surfaces
(Springer Verlag, 2024-05-11) Costa Farràs, Laura; Macías Tarrío, Irene
Let $X$ be a ruled surface over a nonsingular curve $C$ of genus $g \geq 0$. Let $M_H:=M_{X, H}\left(2 ; c_1, c_2\right)$ be the moduli space of $H$-stable rank 2 vector bundles $E$ on $X$ with fixed Chern classes $c_i:=c_i(E)$ for $i=1,2$. The main goal of this paper is to contribute to a better understanding of the geometry of the moduli space $M_H$ in terms of its Brill-Noether locus $W_H^k\left(2 ; c_1, c_2\right)$, whose points correspond to stable vector bundles in $M_H$ having at least $k$ independent sections. We deal with the non-emptiness of this Brill-Noether locus, getting in most of the cases sharp bounds for the values of $k$ such that $W_H^k\left(2 ; c_1, c_2\right)$ is non-empty.
ALGEBRAIC EXPANSIONS OF LOGICS
(Association for Symbolic Logic., 2023-03-01) Campercholi, Miguel; Castaño, Diego Nicolás; Díaz Varela, José Patricio; Gispert Brasó, Joan
An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists!\wedge p=q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AEsubclasses of $\mathcal{Q}$ correspond to certain natural expansions of $L$, which we call algebraic expansions. These turn out to be a special case of the expansions by implicit connectives studied by $\mathbf{X}$. Caicedo. We proceed to characterize all the AE-subclasses of abelian $\ell$-groups and perfect MV-algebras, thus fully describing the algebraic expansions of their associated logics.
Structural completeness in many-valued logics with rational constants
(University of Notre Dame, 2022-08) Gispert Brasó, Joan; Haniková, Zuzana; Moraschini, Tommaso; Stronkowski, Michal
The logics $\mathbf{R} \mathbf{\L}, \mathbf{R} \mathbf{P}$, and $\mathbf{R G}$ have been obtained by expanding $\{L}$ukasiewicz logic $\mathbf{L}$, product logic $\mathbf{P}$, and Gödel-Dummett logic $\mathbf{G}$ with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in $\mathbf{} \mathbf{,} \mathbf{P}$, and $\mathbf{G}$. Namely, $\mathbf{R} \mathbf{L}$ is hereditarily structurally complete. $\mathbf{R} \mathbf{P}$ is algebraized by the variety of rational product algebras that we show to be $\mathcal{Q}$-universal. We provide a base of admissible rules in RP, show their decidability, and characterize passive structural completeness for extensions of $\mathbf{R P}$. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of $\mathbf{R P}$, and this is also the case for extensions of RG, where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of $\mathbf{R G}$ we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is $\mathcal{Q}$-universal.
On the Non-falsity and Threshold Preserving Variants of MTL Logics
(Springer Verlag, 2025-07-09) Esteva Massaguer, Francesc; Gispert Brasó, Joan; Godo i Lacasa, Lluís
In this paper we study the definition and axiomatisation of non-falsity preserving and threshold preserving companions of several extensions of the Monoidal t-norm based fuzzy logic MTL. More in detail, we first extend some recent preliminary results on non-falsity preserving logics, and then we present a new study on threshold-preserving companions of the main three fuzzy logics, Łukasiewicz, Product and Gödel logics.
On Nilpotent Minimum logics defined by lattice filters and their paraconsistent non-falsity preserving companions.
(Oxford University Press, 2025-06) Gispert Brasó, Joan; Esteva Massaguer, Francesc; Godo i Lacasa, Lluís; Coniglio, Marcelo E.
Nilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov’s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, with special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains.
On the role of the fast oscillations in the secular dynamics of the lunar coplanar perturbation on Galileo satellites
(Elsevier B.V., 2025-03-01) Alessi, Elisa Maria; Baldomá Barraca, Inmaculada; Giralt i Oms, Marta; Guàrdia Munárriz, Marcel; Pousse, Alexandre
Motivated by the practical interest in the third-body perturbation as a natural cleaning mechanism for high-altitude Earth orbits, we investigate the dynamics stemming from the secular Hamiltonian associated with the lunar perturbation, assuming that the Moon lies on the ecliptic plane. The secular Hamiltonian defined in that way is characterized by two timescales. We compare the location and stability of the fixed points associated with the secular Hamiltonian averaged with respect to the fast variable with the corresponding periodic orbits of the full system. Focusing on the orbit of the Galileo satellites, it turns out that the two dynamics cannot be confused, as the relative difference depends on the ratio between the semi-major axis of Galileo and the one of the Moon, that is not negligible. The result is relevant to construct rigorously the Arnold diffusion mechanism that can drive a natural growth in eccentricity that allows a satellite initially on a circular orbit in Medium Earth Orbit to reenter into the Earth’s atmosphere.
Activity Theory in Digital Game-Based Learning: A Geometry Case Study
(Serious Games Society, 2025-05-16) Sors Vidal, Oriol; Puig Puig, Anna; Rodríguez Santiago, Inmaculada
Digital Game-Based Learning (DGBL) is a complementary methodology to tra-ditional instruction, yet it often faces conceptual and practical limitations inevolving educational environments. These include the closed nature of gamesand a narrow focus on single competencies. To address these challenges, thisstudy explores DGBL through the third generation of Activity Theory (AT)and applies the Expansive Learning framework. Specifically, we investigatethe following research questions: RQ1:”How does Expansive Learning de-signed in a game influence the learning experience in terms of learning out-comes and engagement?”, and RQ2:”How do game challenges created by stu-dents impact their peers’ learning experience?”. To answer these questions,a quasi-experimental study was conducted with secondary students, includinga control group (players) and an experimental group (players+creators), usingGeoBuild, a geometry game based on Expansive Learning principles. Learn-ing outcomes were assessed via pre- and post-tests, motivation and enjoymentthrough questionnaires, and engagement using in-game analytics and qualitativefeedback. Although all students improved their learning outcomes, the controlgroup outscored the experimental group in the final exam. However, they mademore errors in peer-created challenges, which were harder than those set by theteacher. Challenge completion rates were similar, and students found the expe-rience engaging, suggesting promising grounds for further research.
Mirando hacia el futuro: problemas de frontera libre
(2021-01-01) Ros, Xavier
Las ecuaciones en derivadas parciales (EDPs) son un campo de investigación muy amplio y activo, con importantes conexiones con otros campos como el análisis armónico, la geometría diferencial, el cálculo de variaciones, la teoría de probabilidad, la teoría geométrica de la medida, o la matemática computacional y aplicada. Una de las preguntas más básicas y centrales en el estudio de EDPs es la regularidad: Dada una cierta EDP (o una clase general de EDPs), ¿son regulares todas sus soluciones, o pueden tener singularidades?
On the moduli space of simple sheaves on singular K3 surfaces
(Elsevier Masson SAS, 2025-03-01) Fantechi, Barbara; Miró-Roig, Rosa M. (Rosa Maria)
Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in [6] we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof.
Families of simple Jacobians with many automorphisms
(Foundation Compositio Mathematica, 2025-11) Naranjo del Val, Juan Carlos; Ortega, Angela; Pirola, Gian Pietro; Spelta, Irene
We study an explicit ( $2 g-1$ )-dimensional family of Jacobian varieties of dimension $\frac{1}{2}(d-1)(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g \geqslant 2$. By using a deformation argument, we prove that the generic element of the family is simple. Furthermore, we completely describe their endomorphism algebra, and we show that they admit a rank $\frac{1}{2}(d-1)-1$ group of non-polarized automorphisms. As an application of these results, we prove the generic injectivity of the Prym map for étale cyclic coverings of hyperelliptic curves of odd prime degree under some slight numerical restrictions. This result generalizes in several directions previous results on genus 2 .
Homotopy BV-algebras in Hermitian geometry
(Elsevier, 2024) Cirici, Joana; Wilson, Scott O.
We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative -algebra structure satisfying the degeneration property. In the almost Kähler case, this recovers Koszul's BV-algebra, defined for any Poisson manifold. As a consequence, both the Dolbeault and the de Rham cohomologies of any compact Hermitian manifold are canonically endowed with homotopy hypercommutative algebra structures, also known as formal homotopy Frobenius manifolds. Similar results are developed for (almost) symplectic manifolds with Lagrangian subbundles.
Coloring minimal Cayley graphs.
(Elsevier Ltd., 2025-01-10) García Marco, Ignacio; Knauer, Kolja
In 1978 Babai raised the question whether all minimal Cayley graphs have bounded chromatic number; in 1994 he conjectured a negative answer. In this paper we show that any minimal Cayley graph of a (finitely generated) generalized dihedral or nilpotent group has chromatic number at most 3, while 4 colors are sometimes necessary for soluble groups. On the other hand we address a related question proposed by Babai in 1978 by constructing graphs of unbounded chromatic number that admit a proper edge coloring such that each cycle has some color at least twice. The latter can be viewed as a step towards confirming Babai’s 1994 conjecture – a problem that remains open.
Multi-Objective Reinforcement Learning for Designing Ethical Multi-Agent Environments
(Springer Verlag, 2023-08-23) Rodríguez Soto, Manel; López Sánchez, Maite; Rodríguez-Aguilar, Juan A. (Juan Antonio)
This paper tackles the open problem of value alignment in multi-agent systems. In particular, we propose an approach to build an ethical environment that guarantees that agents in the system learn a joint ethically-aligned behaviour while pursuing their respective individual objectives. Our contributions are founded in the framework of Multi-Objective Multi-Agent Reinforcement Learning. Firstly, we characterise a family of Multi-Objective Markov Games (MOMGs), the socalled ethical MOMGs, for which we can formally guarantee the learning of ethical behaviours. Secondly, based on our characterisation we specify the process for building single-objective ethical environments that simplify the learning in the multi-agent system. We illustrate our process with an ethical variation of the Gathering Game, where agents manage to compensate social inequalities by learning to behave in alignment with the moral value of beneficence.
Acyclic reorientation lattices and their lattice quotients
(Springer Verlag, 2024) Pilaud, Vincent
We prove that the acyclic reorientation poset of a directed acyclic graph D is a lattice if and only if the transitive reduction of any induced subgraph of D is a forest. We then show that the acyclic reorientation lattice is always congruence normal, semidistributive (thus congruence uniform) if and only if D is filled, and distributive if and only if D is a forest. When the acyclic reorientation lattice is semidis- tributive, we introduce the ropes of D that encode the join irreducible acyclic reorientations and exploit this combinatorial model in three direc- tions. First, we describe the canonical join and meet representations of acyclic reorientations in terms of non-crossing rope diagrams. Second, we describe the congruences of the acyclic reorientation lattice in terms of lower ideals of a natural subrope order. Third, we use Minkowski sums of shard polytopes of ropes to construct a quotientope for any congruence of the acyclic reorientation lattice.
L-invariants for cohomological representations of PGL(2) over arbitrary number fields
(2024-05-30) Gehrmann, Lennart; Pati, Maria Rosaria
Let π be a cuspidal, cohomological automorphic representation of an inner form G of PGL2 over a number field F of arbitrary signature. Further, let p be a prime of F such that G is split at p and the local component πp of π at p is the Steinberg representation. Assuming that the representation is noncritical at p, we construct automorphic L-invariants for the representation π. If the number field F is totally real, we show that these automorphic L-invariants agree with the Fontaine–Mazur L-invariant of the associated p-adic Galois representation. This generalizes a recent result of Spieß respectively Rosso and the first named author from the case of parallel weight 2 to arbitrary cohomological weights.
A monotonicity theorem for subharmonic functions on manifolds
(Elsevier B.V., 2025-07-07) Kulikov, Aleksei; Nicola, Fabio; Ortega Cerdà, Joaquim; Tilli, Paolo
We provide a sharp monotonicity theorem about the distribution of subharmonic functions on manifolds, which can be regarded as a new, measure theoretic form of the uncertainty principle. As an illustration of the scope of this result, we deduce contractivity estimates for analytic functions on the Riemann sphere, the complex plane and the Poincaré disc, with a complete description of the extremal functions, hence providing a unified and illuminating perspective of a number of results and conjectures on this subject, in particular on the Wehrl entropy conjecture by Lieb and Solovej. In this connection, we completely prove that conjecture for $SU$(2), by showing that the corresponding extremals are only the coherent states. Also, we show that the above (global) estimates admit a local counterpart and in all cases we characterize also the extremal subsets, among those of fixed assigned measure.
Boundary dynamics in unbounded Fatou components.
(American Mathematical Society (AMS), 2025-02-11) Jové Campabadal, Anna; Fagella Rabionet, Núria
We study the behaviour of a transcendental entire map $f: \mathbb{C} \rightarrow \mathbb{C}$ on an unbounded invariant Fatou component $U$, assuming that infinity is accessible from $U$. It is wellknown that $U$ is simply connected. Hence, by means of a Riemann map $\varphi: \mathbb{D} \rightarrow U$ and the associated inner function $g:=\varphi^{-1} \circ f \circ \varphi$, the boundary of $U$ is described topologically in terms of the disjoint union of clusters sets, each of them consisting of one or two connected components in $\mathbb{C}$, improving the results in [BD99; Bar08]. Moreover, under mild assumptions on the location of singular values in $U$ (allowing them even to accumulate at infinity, as long as they accumulate through accesses to $\infty)$, we show that periodic and escaping boundary points are dense in $\partial U$, and that all periodic boundary points accessible from $U$. Finally, under similar conditions, the set of singularities of $g$ is shown to have zero Lebesgue measure, strengthening substantially the results in [EFJS19; ERS20].

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